Sen. Richard J. Durbin, D-Ill., would provide few details of how he and fellow immigration "gang of eight" senators planned to respond to the deluge of amendments at a markup later this week.

Durbin told reporters that the eight senators who drafted the proposal did not make a "blood oath" over accepting or rejecting amendments, but they were mindful of the possibility that contentious proposals could derail the bill.

"We've got to be careful. We'll sit down before the markup, after we see the amendments and talk about problems," Durbin said.

"Sen. Leahy's starting this week, and we're likely to spend a lot of hours together on this markup," Durbin said. "My guess is, knowing the dynamics of senatorial conduct, people get worn out after a while and we're counting on that."

Republican Sen. Orrin G. Hatch of Utah filed 20 amendments, on subjects ranging from payment of back taxes by individuals seeking legal status to an expansion of the number of H-1B visas for high-skilled workers.

"I hope that we don't end up adopting amendments on the vain belief that picking up one more senator on one side or the other will pass the bill and lose our basic agreement," Durbin said in response to a question about getting Hatch's vote. "We've got to keep the strength of this core agreement in place."

Amendments poured in to the Judiciary Committee on Tuesday afternoon, though aides cautioned that merely drafting an amendment doesn't mean it will be put to a vote at the committee level.

Leahy filed two versions of his Uniting American Families Act as amendments to the immigration overhaul. One applies broadly to same-sex partnerships, and the other applies more narrowly to gay marriages.

“If people disagree with this amendment, vote against it. That’s simple enough,” Leahy told Vermont Public Radio on Monday. “We’re going to have votes on everything and vote yes, vote no. Don’t go running off and saying ‘Oh, I can’t vote for something I wasn’t going to vote for anyway because I don’t like some part of it.’”

Durbin said he and other gang of eight Democrats were aware of potential issues with the Leahy amendment on the Republican side, but he said the Supreme Court's upcoming ruling on the constitutionality of the Defense of Marriage Act could alter the voting dynamic.

"The DOMA ruling could change this whole debate," Durbin said, noting that if the court tosses the law, it could result in imposing "obligations on our federal government to those who are [in] same gender marriage."